Looking at the device - it's kind of limited on audio codecs it supports:
"Audio Formats - MP3, AC3 (Dolby® Digital Encoding), WAV, OGG, WMA"
So - unless you have iMovie 09 and it supports more audio codecs in the movie containers; or unless the Screenplay Director supports more audio codecs in the video containers it supports (which I doubt at this point from your description) I'm thinking you'll need to export at the best settings you can, then transcode.
The only option I can think of is maybe exporting to a quicktime .mov and see if it lets you set the audio to mp3.
Basically - you need to have a video file with a container that is supported by Screenplay Director (File Types - .mkv, .avi, .asf, .iso, .vob, .mp4, .mov, .wmv, .flv, .ifo) using a video format that it likes (Video Formats - MPEG-1, MPEG-2 (AVI/VOB), MPEG-4 (AVI/DivX®/XViD), H.264, WMV, AVCHD) also containing audio that it likes (Audio Formats - MP3, AC3 (Dolby® Digital Encoding), WAV, OGG, WMA) - if you can't find all 3 that match up in iMovie on the export (it may take some looking around in the audio options on each export container supported in iMovie) then export the best you can so it plays right on the Mac, then use Handbrake to do a transcode and in the audio section make sure to select your output audio so it matches one of the formats the device likes.
Honestly tho, if it's still new and can be returned, I'd probably look at a different device that supports more audio/video combinations ( WD TV: WD TV Live HD Media Player ( WDBAAN0000NBK )
- Popcorn Hour - Welcome To Popcorn Hour
- etc. - but check reviews first to make sure it'll work with your files. Personally, I have a Mac Mini hooked into my home theater working to play my media files). AAC is a pretty standard audio codec (and I think it's one of the defaults used by imovie on export) and AAC does not appear to be supported by your device.